Question

A grenade having mass of 10kg flying horizontally with velocity of 10 m/s into two fragment .The larger fragment has velocity of 25 m/s in the direction of the grenade .the smaller fragment has velocity of 12.5 m/s in the opposite direction.the masses of the fragments are ??????????????????????????????????????????????????????????

Answer 1

A grenade having mass of $10\mathrm{kg}$ flying horizontally with velocity of $10~\mathrm{m/s}$ into two fragments. The larger fragment has velocity of $25~\mathrm{m/s}$ in the direction of the grenade. the smaller fragment has velocity of $12.5~\mathrm{m/s}$ in the opposite direction. The masses of the fragments are?

The law of conservation of momentum:

$$M v _ {0} = m _ {1} v _ {1} + m _ {2} v _ {2}$$

Sum of mass of fragments equals:

$$M = m _ {1} + m _ {2}$$

From second: $m_{1} = M - m_{2}$, substitute to first:

$$M v _ {0} = (M - m _ {2}) v _ {1} + m _ {2} v _ {2}$$ $$m _ {2} = M \frac {v _ {0} - v _ {1}}{v _ {2} - v _ {1}} = 1 0 \frac {2 5 - 1 0}{2 5 - (- 1 2 . 5)} k g = 4 k g$$

And

$$m _ {1} = M - m _ {2} = M - M \frac {v _ {0} - v _ {1}}{v _ {2} - v _ {1}} = M \frac {v _ {2} - v _ {0}}{v _ {2} - v _ {1}} = 1 0 \frac {- 1 2 . 5 - 1 0}{- 1 2 . 5 - 2 5} = 6 k g$$

Answer: 6 and $4\mathrm{kg}$